This Venn diagram might help to visualize the relation between the different fields:
The image is from the free deep learning book by Ian Goodfellow, Yoshua Bengio and Aaron Courville. As you said machine learning is indeed a subset of Artificial intelligence. Artificial intelligence is since its origins a very broad framework with a strong overlap with computer science, neuroscience, game theory, reinforcement learning, linguistics, etc. Computer vision can in general be considered a part of artificial intelligence. However, computer vision comes in various flavors and forms and some people in the field might not be fond of putting their work under the 'AI' umbrella. Data science conceptually overlaps with many of the methods used within AI but it is more focused on statistics, data analytics, modeling, and data mining.
In industry being a data scientist often means 'generating insights from data' (eg via AB testing) while working as something with AI in the title involves some kind of deep learning (eg for natural language understanding).